Minimum time generation of SU(2) transformations with asymmetric bounds on the controls

TL;DR

This paper determines the minimum time to generate SU(2) transformations in a two-level quantum system with asymmetric control bounds, considering a constant drift and three independent controls, providing a complete characterization of optimal strategies.

Contribution

It introduces a comprehensive analysis of minimum-time control for SU(2) transformations with asymmetric control bounds, extending previous symmetric-bound results.

Findings

Complete characterization of reachable sets

Optimal control strategies for any target transformation

Analysis applicable to systems with asymmetric control constraints

Abstract

We study how to generate in minimum time special unitary transformations for a two-level quantum system under the assumptions that: (i) the system is subject to a constant drift, (ii) its dynamics can be affected by three independent, bounded controls, (iii) the bounds on the controls are asymmetric, that is, the constraint on the control in the direction of the drift is independent of that on the controls in the orthogonal plane. Using techniques recently developed for the analysis of SU(2) transformations, we fully characterize the reachable sets of the system, and the optimal control strategies for any possible target transformation.